Related papers: Modelling collective cell migration in a data-rich…
Hybrid modeling provides an effective solution to cope with multiple time scales dynamics in systems biology. Among the applications of this method, one of the most important is the cell cycle regulation. The machinery of the cell cycle,…
Machine learning (ML) has emerged as a pervasive tool in science, engineering, and beyond. Its success has also led to several synergies with molecular dynamics (MD) simulations, which we use to identify and characterize the major…
In the present paper, our goal is to establish a framework for the mathematical modelling and the analysis of the spread of an epidemic in a large population commuting regularly, typically along a time-periodic pattern, as is roughly…
Understanding kinetics and thermodynamics profile of biomolecules is necessary to understand their functional roles which has a major impact in mechanism driven drug discovery. Molecular dynamics simulation has been routinely used to…
Molecular dynamics (MD) has become a powerful tool for studying biophysical systems, due to increasing computational power and availability of software. Although MD has made many contributions to better understanding these complex…
At its core, the physics paradigm adopts a reductionist approach, aiming to understand fundamental phenomena by decomposing them into simpler, elementary processes. While this strategy has been tremendously successful in physics, it has…
Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
This paper is a first step to chase the ambitious objective of developing a mathmatical theory of living systems. The contents refer modeling large systems of interacting living entities with the aim of describing their collective behaviors…
There are numerous scenarios in which populations of cells migrate in crowded environments. Typical examples include wound healing, cancer growth and embryo development. In these crowded environments cells are able to interact with each…
Scientific Machine Learning (SciML) is a recently emerged research field which combines physics-based and data-driven models for the numerical approximation of differential problems. Physics-based models rely on the physical understanding…
Most modeling approaches lie in either of the two categories: physics-based or data-driven. Recently, a third approach which is a combination of these deterministic and statistical models is emerging for scientific applications. To leverage…
The excessive amounts of data generated by devices and Internet-based sources at a regular basis constitute, big data. This data can be processed and analyzed to develop useful applications for specific domains. Several mathematical and…
Can machine learning help discover new mathematical structures? In this article we discuss an approach to doing this which one can call "mathematical data science". In this paradigm, one studies mathematical objects collectively rather than…
As new technologies move to the fore, our understanding of the world may seem to have shrunk in comparison, for despite new developments in research, much of it is reduced or rather, abstracted for marketability. Thus, the purpose of this…
Computational multiscale methods for analyzing and deriving constitutive responses have been used as a tool in engineering problems because of their ability to combine information at different length scales. However, their application in a…
The modeling of the spreading of communicable diseases has experienced significant advances in the last two decades or so. This has been possible due to the proliferation of data and the development of new methods to gather, mine and…
Within the biological, physical, and social sciences, there are two broad quantitative traditions: statistical and mathematical modeling. Both traditions have the common pursuit of advancing our scientific knowledge, but these traditions…
A variety of computational models have been developed to describe active matter at different length and time scales. The diversity of the methods and the challenges in modeling active matter---ranging from molecular motors and cytoskeletal…
Molecular dynamics simulations are an important tool for describing the evolution of a chemical system with time. However, these simulations are inherently held back either by the prohibitive cost of accurate electronic structure theory…